It really depends on what type of information is sought.
The linked question specifically mentions references. If a company asks for a reference, either written, or a person to contact, they ARE looking for subjective assessment of a persons qualities. Usually leaders of the employee can be used as a reference, but this is usually a personal agreement between two employees.
Potential referees should be approached by the employee to agree to be a reference. In doing so, the employee is giving permission for the referee to act as one. If an employee is randomly contacted, they should decline to offer any information.
This is different from a contact in order to provide proof of employment. The amount of information given out then will depend heavily on legislation, but typically in large firms they will give out the bare minimum required by law. This is usually handled by the HR department. The previous employer would not make an assertions that they could not defend in court. They would not validate the status of degrees. They want to say as little as possible.
With smaller companies, the difference between proof of employment and reference can be blurred.